The mayor of New York has reached an agreement with Uber, dropping plans for a strict cap on its growth that would have limited the number of cars available in the city.

The agreement follows a bitter public feud between Uber and the administration of Mayor Bill de Blasio. The city had blamed Uber for slowing traffic in Manhattan and proposed a 1% cap on the growth of Uber and other ride-hailing services.

Uber shot back with a spoof "de Blasio" mode in its app that displayed the...